Local and Global Aspects of Lie Superposition Theorem
Local and Global Aspects of Lie Superposition Theorem
复制标题
李叠加定理的局部和全局方面
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Morales
中科院分区：
文献类型：
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作者：
D. Blázquez;J. Morales
本文给出了一类常微分方程在经典意义上存在解叠加律的全局条件。这就完成了著名的李氏叠加定理。我们引入了前传递李群作用和李维索系统的严格概念。证明了一个常微分方程当且仅当其包络代数是由一个前传递李群作用的基本域张成的。我们讨论了叠加律与微分伽罗瓦理论的关系，并对李的经典结果进行了回顾。数学学科分类2000:34M15, 35C05, 34M35, 34M45。
In this paper we give the global conditions for an ordinary differential equation to admit a superposition law of solutions in the classical sense. This completes the well-known Lie superposition theorem. We introduce rigorous notions of pretransitive Lie group action and Lie-Vessiot systems. We prove that an ordinary differential equation admit a superposition law if and only if its enveloping algebra is spanned by fundamental fields of a pretransitive Lie group action. We discuss the relationship of superposition laws with differential Galois theory and review the classical result of Lie. Mathematics Subject Classification 2000: 34M15, 35C05, 34M35, 34M45.